Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
2.2.1 Transforming between ITRF and ICRF
Th
e transformation from the ITRF coordinate system
(
x
)
to the ICRF coordinate
sy
stem
(
X
)
at epoch
t
is (McCarthy, 1996, p. 21; Mueller, 1969, p. 65):
R
(t)
R
(t)
x
X
R
(t)
=
(2.9)
where
R
(t)
=
P
(t)
N
(t)
(2.10)
R
(t)
=
R
3
(
−
GAST
)
(2.11)
R
(t)
=
R
1
(y
p
)
R
2
(x
p
)
(2.12)
[22
P
(t)
=
R
3
(
ζ
)
R
2
(
−θ
)
R
3
(z)
(2.13)
Lin
—
7.2
——
Nor
PgE
N
(t)
=
R
1
(
−
ε)
R
3
(
∆ψ
)
R
1
(ε
+ ∆
ε)
(2.14)
with
2306
.
2181
t
0
.
30188
t
2
0
.
017998
t
3
ζ =
+
+
(2.15)
2306
.
2181
t
1
.
09468
t
2
0
.
018203
t
3
z
=
+
+
(2.16)
2004
.
3109
t
0
.
42665
t
2
0
.
041833
t
3
θ =
−
−
(2.17)
[22
17
.
1996 sin
(
0
.
2062 sin
(
2
∆ψ =−
Ω
)
+
Ω
)
(2.18)
1
.
3187 sin
(
2
F
−
−
2
D
+
2
Ω
)
+···+
d
ψ
9
.
2025 cos
(
0
.
0895 cos
(
2
∆
ε
=
Ω
)
−
Ω
)
(2.19)
0
.
5736 cos
(
2
F
+
−
2
D
+
2
Ω
)
+···+
dε
84381
.
448
46
.
8150
t
0
.
00059
t
2
0
.
001813
t
3
ε
=
−
−
+
(2.20)
w
here
t
is the time since J2000.0, expressed in Julian centuries of 36,525 days. The
ar
guments of the trigonometric terms in (2.18) and (2.19) are integer multiples of
th
e fundamental periodic elements
l
,
l
,
F
,
D
, and
Ω
, resulting in nutation periods
th
at vary from 18.6 years to about 5 days. Of particular interest is
, which appears
as
an argument in the first term of these equations. The largest nutation, which
al
so has the longest period (18.6 years), is a function of
Ω
, which represents the
rotation of the lunar orbital plane around the ecliptic pole. The complete set of
nutations contains more than 100 entries. The amplitudes of the nutations are based
on geophysical models of the earth. Currently, the IAU 2000 precession and nutation
Ω
